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Journals and Conferences

In this paper we introduce the notion of tolerance in connection with Helly type theorems and prove, using the Erdős-Gallai theorem, that any Helly type theorem can be generalized by relaxing the… (More)

Let p ≥ q ≥ d+1 be positive integers and let F be a finite family of convex sets in Rd. Assume that the elements of F are coloured with p colours. A p-element subset of F is heterochromatic if it… (More)

Let R and B be disjoint point sets such that R ∪ B is in general position. We say that B encloses by R if there is a simple polygon P with vertex set B such that all the elements in R belong to the… (More)

Given a set of n points on the plane colored with k ≤ n colors, the Trip Planning Problem asks for the shortest path visiting the k colors. It is a well-known NP-hard problem. We show that under some… (More)

A carousel is a dynamical system that describes the movement of an equilateral linkage in which the midpoint of each rod travels parallel to it. They are closely related to the floating body problem.… (More)

Wepresent a RainbowRamsey version of thewell-knownRamsey-type theoremof Richard Rado. We use new techniques from the Geometry of Numbers. We also disprove two conjectures proposed in the literature.… (More)

The problem of computing the chromatic number of Kneser hypergraphs has been extensively studied over the last 40 years and the fractional version of the chromatic number of Kneser hypergraphs is… (More)